Flotation and free surface flow in a model for subglacial drainage. Part 2. Channel flow

Abstract

We present a new model of subglacial drainage incorporating flow in a network of channels and a porous sheet, with water exchange between the two determined by pressure gradients. The sheet represents the average effect of many linked cavities, whilst the channels emerge from individual cavities that enlarge due to dissipation-induced melting. The model distinguishes cases when the water pressure drops to zero, in which case it allows for the drainage space to be only partially filled with water (free surface flow), and when the pressure reaches the ice overburden pressure, in which case it allows for uplift of the ice to whatever extent is needed to accommodate the water (flotation). Numerical solutions are found for a one-dimensional flow-line version of the model. The results capture typically observed or inferred features of subglacial drainage systems, including open channel flow at the ice margin, seasonal channel evolution, and high water pressures and uplift of the ice surface driven by rapid changes in water supply.

Oscillatory subglacial drainage in the absence of surface melt

“…Ng, 1998;Hewitt and Fowler, 2008;Schuler and Fischer, 2009;Hewitt et al, 2012). Denoting conduit cross section by S(x, t), effective pressure by N (x, t) and discharge by Q(x, t), where x is downstream distance and t is time, we put…”

“…For computational tractability and in keeping with many other similar drainage models (e.g. Werder et al, 2013), we do not impose the upper and lower bounds on water pressure considered in Schoof et al (2012) and Hewitt et al (2012).…”

“…This can be done by recognizing that (see also Hewitt et al, 2012) Q(x) = x 0 m(x ) dx = mx in steady state, and rewriting the steady-state version of Eq. (2) as a first-order nonlinear differential equation for N. This is done by solving for S in Eq.…”

“…A naïve application of the parameter values in Schoof (2010) combined with geometrical parameters that are representative for South Glacier results in effective pressures that are significantly larger than those observed in the field; in fact, these are significantly larger than ice overburden on the glacier, implying that basal conduits should only be partially filled Hewitt et al, 2012). Overprediction of effective pressures is a known phenomenon in subglacial drainage models (Schuler andFischer, 2009), andHooke et al (1990) suggest that the assumption of semicircular conduits in computing creep closure rates is at fault.…”

A double continuum hydrological model for glacier applications

“…Recently published subglacial hydrological models take into account inefficient and efficient components for the drainage system (Pimentel et al, 2010;Schoof, 2012;Hewitt et al, 2012;Werder et al, 2013). Following the work initiated by Flowers and Clarke (2002a), a sediment layer is used to model the inefficient drainage system (IDS), and, rather than actually modelling a network of channels to represent the efficient drainage system, we use an equivalent porous layer (EPL).…”